This paper addresses the problem of statistical inference for latent continuous-time stochastic processes, which is often intractable, particularly for discrete state space processes described by Markov jump processes. To overcome this issue, we propose a new tractable inference scheme based on an entropic matching framework that can be embedded into the well-known expectation propagation algorithm. We demonstrate the effectiveness of our method by providing closed-form results for a simple family of approximate distributions and apply it to the general class of chemical reaction networks, which are a crucial tool for modeling in systems biology. Moreover, we derive closed form expressions for point estimation of the underlying parameters using an approximate expectation maximization procedure. We evaluate the performance of our method on various chemical reaction network instantiations, including a stochastic Lotka-Voltera example, and discuss its limitations and potential for future improvements. Our proposed approach provides a promising direction for addressing complex continuous-time Bayesian inference problems.

翻译：本文针对潜在连续时间随机过程的统计推断问题展开研究，该类问题通常难以求解，尤其对于由马尔可夫跳变过程描述的离散状态空间过程。为克服这一难题，我们提出了一种基于熵匹配框架的新型可处理推断方案，该方案可嵌入经典的期望传播算法。通过为简单近似分布族提供闭式结果，我们展示了该方法的有效性，并将其应用于化学反网络这一系统生物学建模的核心工具。此外，我们利用近似期望最大化过程推导出基础参数点估计的闭式表达式。我们通过多个化学反应网络实例（包括随机Lotka-Volterra模型）评估了该方法性能，并讨论了其局限性及未来改进方向。所提出的方法为解决复杂连续时间贝叶斯推断问题提供了有前景的研究方向。